Geodesic
On an identity for stochastic integrals
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 761-765

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A sufficient condition is obtained for the identity $$ \mathbf{M}\exp\biggl\{\int_0^T f(t,\omega)\,dw(t)-\frac12\int_0^T f^2(t,\omega)\,dt\biggr\}=1 $$ to hold. (Here $\int_0^T f(t,\omega)\,dw(t)$ is the stochastic integral with respect to a Wiener process $w(t)$.) This condition is shown to be close to a necessary one. 
@article{TVP_1972_17_4_a16,
     author = {A. A. Novikov},
     title = {On an identity for stochastic integrals},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {761--765},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a16/}
}
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A. A. Novikov. On an identity for stochastic integrals. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 761-765. http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a16/